SLAC -PUB - 3444 September 1984 T/E

CALCULATION OF EXCLUSIVE DECAY MODES OF THE TAU*

FREDERICK J. GILMANAND SUNHONG RHIE

Stanford Linear Accelerator Center

Stanford University, Stanford, California, Qa3O5

ABSTRACT a~-

We update the calculation of the decays of the T lepton into various modes

using recent data on electron-positron annihilation into .hadrons plus bounds

that follow from isotopic spin conservation. Comparison is made with exclusive

branching ratio data and inclusive charged prong distribution measurements in

T decays and the difficulty in accounting for all the one charged-prong decays as

a sum of exclusive decay modes is discussed.

Submitted to Physical Review D

* Work supported by the Department of Energy, contract DE - AC03 - 76SF00515

. ..1

1. Introduction

The observed properties of the r lepton are consistent with it being a sequen-

tial lepton’ -a heavier version of the electron or muon, with its own neutrino

partner, u,. Particularly with the coming into operation of the PETRA/PEP

generation of electron-positron colliding beam machines, the separation of r-r+

pair production from production of hadrons has become very clean and more

accurate measurement of some properties of the r have become possible. In par-

ticular, measurements of the 7 lifetime2 show that the strength of the charged

weak current coupling between r and ur is consistent with being of universal

strength, further supporting the standard assignment of the r (and vr). _ c-

The clean separation of r events has allowed the accurate measurement of

the distribution of charged-prong multiplicity in its decay.’ In this regard it is

interesting to reexamine the branching ratios for r decay into each of its exclusive

decay modes, both to check that the individual modes occur at the predicted rate

and to see that the exclusive modes which yield one charged-prong, three charged-

prongs, . . . sum up to give the measured inclusive charged-prong multiplicities.

In this way we can perform a further check to see if everything is attributable to

the decays expected in the standard model, or if there is some small percentage

of r decays which is “unexplained”.

In the next section we go through r decays mode by mode and establish their

branching ratio relative to that for r + u, ep’, by using experimental data (from

outside of r decay) wherever possible:4’5 rr- + ~1~ Do to determine r- --) u, 7r-,

e+e- + 47r to determine r --) u, 47r, etc. In a number of cases we work out bounds

that follow from conservation of isotopic spin that allow us to put limits on as

yet unmeasured branching ratios, e.g., we show that the rate for r- --) u7 7r-47r”

2

can be bounded in terms of the rate for r- + u, 3z-2~~ (for which an excellent

experimental upper bound exists).

In Section 3 we compare the sum of the exclusive modes with the inclusive

charged-prong multiplicity measurements. We find that it is difficult to account

for all the one charged-prong decays and still be consistent with the number of

decays going into three charged prongs. We then examine various “cures” for

this problem ranging from statistical fluctuations in some measurements to new

physics and indicate how various possibilities may be eliminated.

2. Calculation of T Decay Modes

We calculate r decay modes assuming the standard model with a V-A in-

- teraction of universal strength between the r and ur , whose masses we take to

be6 1784 MeV and zero, respectively. With an eye to the next section where

we compare the sum of exclusive modes with inclusive charged-prong branching

ratios, in a number of cases the breakdown of a given mode into charged-prong

multiplicities will be examined in some detail.

(4 r- --) u,e-ii,

Neglecting the mass of the electron, the width for this decay is

Ggrn: I?(7 + uze-P,) = - =

1 1927rs 1.595 x lo-l2 set ’ 0)

The lifetime of the r is then

rr = (1.595 x lo-l2 set) B(r -+ u, eve) . (2)

The present most accurate measurement2 of the lifetime, (2.86 f 0.16 f 0.25) x

lo-l3 set implies B(r + u, ev,) = 17.9 f 1.0 f l.S%, in agreement with the

3

c

direct measurements” of this branching ratio. Conversely, to within the errors

of the branching ratio measurements, the predicted lifetime in Eq. (2) agrees

with the measured one, providing support for the standard model assumptions

that leads to Eqs. (1) and (2). W e shall return in the next section to the question

of how much B(r + u, ep,) can be “stretched” within the experimental errors.

W e will normalize all other calculations of decay widths to the theoretical value

for I’(r- + u, e- t7,) in Eq. (1).

m r- + u7p--i7p

Taking account of the mass of the muon, we have

qr + ur P-- L/b) = w G’m9 F(m,/m,) , (3)

where

F(A) = 1 - 8A2 + 8A6 - A8 - 12A44k A2 .

Thus

r( r+u7p-v) Ir = F(mp/m,) = 0.97 . r (7 -+ ur e- 17,)

(Cl r- + ur7r-

The strength of the pion’s coupling to the axial-vector current is directly deter-

m ined in the well-measured.pion decay, ?r- + ~1~ vP. Exactly the same quantity,

fir cos 8,, is relevant in 7- + u, 7rr-: 495

(D) r- + z+K-

Just as for r- + ur zr- , the quantity of relevance, fK sin 8,, is directly measured

a -3 4

elsewhere and very accurately so, in the dominant decay of the charged kaon,

K- + p- vP. Inserting this information6 gives

l?- + ur K-) = (fK Sine,]2 12r2 r (7- -+ U, e- n,) 4 [ -1 1 _ ml 2 = o 03g5

rn: ’ . (5)

(E) r- + uz 7r-7r”

Here the strength of the charged vector current coupling to ~IT?T can be related, via

the conserved-vector-current hypothesis, to that of the electromagnetic (neutral

vector) current to 7r7r. The latter is measured by a(e+e- --) 7 + r+n-). The

precise relation between the two processes 495 is

. a- a r(7- -+ uT 3f-7r”)

m, 3

- qr- + ur e- De) = 27r ar2rnF / dQ2Q2(mf - Q2)2(mf + 2Q2)~e+e-+~+~-(Q2) ,

(6) where the integration variable Q is the center-of-mass energy of the e+e- (= the

invariant mass of the zz pair).

Of course the zz system is dominated by the p resonance and an approximate

result for I’(r- + ur zr-zo) can be obtained4 from computing r- --) u, p- in

the narrow resonance approximation with the coupling to the vector current

extracted from e+e- + p” experiments. A more accurate result is obtained by

integrating directly over the e+e- ---) zz cross section (or actually a fit to them)

using Eq. (6). With the present r mass, one finds7

r(7- + U, ~~0)

r CT- -+ U, e- i7J = 1.23 ,

with an error which is due principally to the possible overall normalization error

in measurement of the e+e- + z-‘-z- cross sections.

5

(F) r- + ur (Kr)-

Just as the RX system is dominated by the p, we expect this Cabibbo-suppressed

decay to be dominated by the K*(890), as is indeed observed experimentally.6

The rate can be obtained from that for r- ---) u, p- by multiplying by tan2 8, due

to the strangeness-changing current and

(1 - m&/mf)2 (1 + 2mR./mf)/[(l- m2,/mf)2 (1 + 2m;/mf)]

from phase space, aside from SU(3) break’ g m in the coupling strengths to the

respective vector currents.4 This yields the prediction

r CT- j ur K*-) r(7- -+ u, e- f7,)

= 0.058 .

If we incorporate SU(3) breaking by setting’ g&./m&. = gi/rnz, then the pre-

dict ion becomes

I+- --+ u&*-) r(7- -+ ur e- vc)

= 0.079 .

Because of the decay Kg --) ~F+x-, two ninths of the decays r- + u, (Kx)- will

appear as decays with three charged-prongs.

(G) r- ---) ur (47r)-

Inasmuch as this decay proceeds through the vector current, we can again directly

relate the decay rate to an integral over e+e- cross sections, as in Eq. (6). There

are two possible final states in e + e - , 27rr-27rr+ and 7r-7r+27r”, and two in r decay

as well, ur 27rr-7r+7r” and ur 7r-37r”. The constraint of being produced by different

I3 components of the same I = 1 weak current forces one linear relation between

the rates for producing the respective charge states at each 47r invariant mass. As

6

a result, not only can we write the r- -+ ur (4n)- total decay rate as an integral

over Q~+~--,~~, but more specifically:7

a

lY(7- + U, r-3~~) m,

3 r(7- -+ u, e- V,) = 27r a2m$! /

dQ2Q2(mf - Q2)2 0

and

x (mf + 29’) f ~,+,-+2~-2r+ 2 (Q )]

a

r(7- + U, 2c7r+7r”) m,

3 I?&- -+ ur e- VT) = 2aa2m8, /

dQ2Q2(m: - Q2)2 0

The e+e- + 47r cross sections are dominated by the p’ resonance and rough

results may be obtained by approximating the integrand using a single narrow

resonance. This is somewhat dangerous in that the mass (- 1550 MeV) and width

(- 300 MeV) of the p’ make the factor (mf - Q2)2 (rn: + 2Q2) vary strongly over

the resonance, considerably distorting its shape in r decay.g

A more accurate result for r(r ---) ur4~) can be obtained by integrating di-

rectly over the e+e- cross sections. Recent data lo-l2 for e+e- --) 27r+27rr- are

shown in Fig. 1, and they represent a considerable improvement, both with re-

spect to statistics and systematics, over the data that was available for a previous

calculation of r (7 + u, 47r). 7 Carrying out the integration using the curve drawn

through the data in Fig. 1 gives

a m, 3

27r a2m8 / dQ2Q2(mf - Q2)‘(mf + 29’) oe+e-+2r-2r+(Q2) = O-11 - (11)

?O

7 * ..Y

Unfortunately the situation with respect to the data from e+e- + x~~-?T~T’

is not as good. The data 10’12’13from recent experiments are shown in Fig. 2 along

with a dashed curve which passes through the data below Q = 1.4 GeV and is

scaled up from the curve for e+e- + 27r-27r+ in Fig. 1. It lies above much of

the available data for Q > 1.4 GeV. If the dashed curve represented the data

a m, 3

27r cx2ma / dQ2Q2(mf - Q2)‘(mf + 2Q2)0e+e-+r+r-2r0(Q2) = 0.25 . (12~)

7 0

The solid curve, which is a much better representation of the data gives

a m, 3

_ c- 2~ cy2mg I dQ2Q2(mf - Q2)2(mf + 2Q2)oe+e-+x+R-2ro(Q2) = 0.22 . (12b)

rO

while taking the integration only up to Q = 1.4 GeV (certainly a minimum value

for the integral) yields

(1.4 Get’)’ 3

21r a2ma / dQ2Q2b: -Q2)2(mf+2Q2)o,+,-+r+T-z,o(Q2) = 0.13. (12C)

r 0

We will use (12a) and (12~) as bracketing the actual value’of the integral, whose

value we take as that given in (12b).

If we now insert the numerical integration results in Eqs. (11) and (12) back

into Eq. (10) we find

qr- + h 7r-37r0) = o 055 lY(7- -+ ur e-D,) ’ ’

I-(7- + I+ 27r-7rr+7r0) I?(T- -+ ur e-Fe)

= 0.275 ,

(134

W)

and the sum,

8

w- + UT M-1 = 0 33 r(7- + ure-iT7,) . * WC)

The result for the one charged-prong decay r- --) V, 7rr-37r” in Eq. (13a) is rather

certain as it depends only on the integral over the well measured cross section

for e+e- + 27r+27rr- . The numerical result in Eq. (13b) is more uncertain, but

only varies from 0.185 to 0.305 if we use the extreme values for the cross section

for e+e- + 7r+7r-27r” discussed above to bracket the data in Fig. 2.

These results, which correspond to a - 6% branching ratio for r- + u, (47r)-

are 30% to 50% smaller than values7 reported a number of years ago. This is

_ a-- almost entirely due to the change in experimental data for e+e- --) 4n.

The 37r system is generated through the axial vector current and may have Jp =’

O- or l+. There is no other directly measured quantity which can be used to

predict the branching ratio for this mode, which is presumably dominated by the

A1 and possible K’ resonances.” Older calculations15 led to branching ratios of

order 10% for r- + u, A,, in very rough accord with the data.6’14 Inasmuch as

these predictions should only be trusted at the factor of two level, they are now

superceded for our purposes by the rather accurate measurements, particularly

of r- + UT or-?f+, which now exist. 14

Independent of dynamics, isotopic spin forces an important constraint on the

different 37r charge states. Since the total isospin is one, it follows that in the

decay r- + u7 (37r) -

l/5 I fl = 7r-7r0R0

< 112 , all (37r)- - (144

9

and

l/2 I f3 = 27r-7r+

< 415 all (37r)- -

Thus the number of three charged-prong 7 decays must be greater than that of

one charged-prong decays when r- -+ u, (37r)-, something which will have a role

to play in the next section.

(I) r- --) ur (5x)-

Although theoretical estimates’e of the rate for r- ---) ur (57r)- exist, this decay

has yet to be observed and there is no independent way to experimentally de-

termine the strength of the axial-vector current to five pion transition which is

involved here. Standard methods ” _ c- do allow one to find the constraints due to

isotopic spin conservation:

owl= 7r-47re

< 3/10 , all (57r)- -

8135 5 f3 = 27r-7r+27r0 < 1 all (57r)- - ’

OHS= 3?r--2~+

< 24135 . all (57r)- -

054

(154

All of this decay mode could go into three charged-prongs (e.g., r- +

u, mop-), as implied in (14b), and hence the very good experimental limit ‘* on

five charged-prong decays of the r does not necessarily imply the overall branch-

ing ratio for r- + u, (57r)- is very small. However, for our purposes later we

will want to have a bound on the one charged-prong mode r- + u, 7rr-47r”, and

this is obtainable from an upper limit on r- + u, 3~~2~~.

For this purpose we need not the bound in Eq. (14), but the joint distribution

on the fraction of 7rr-47r” versus the fraction of 3x-2~~. The region allowed by

isotopic spin conservation for these two fractions is shown in Fig. 3, and from

this we see that

f3r-2x+ > 4,3

fr4ro - *

Consequently we have the bound

B(r- -+ ur 7r-47r”) 5 (3/4) B(r- + u, 3?r-2~+)

2 3/4 B(T- --) 5 charged-prongs) .

(J) r- + ur (67r)-

In this case we can use either isotopic spin conservation plus the experimental

bound l8 on T --) 5 charged prongs to bound either the decay rate for the complete . a-

mode r- + ur (67r)- or the particular decay T- + u, 7r-57r”, for the constraints

from isotopic spin forcel’

owl= 7r-57P

all (67r)- < - 9135 ,

115 I f3 = 2~r--lr+3~r’ all (67r)- I 415 ,

115 L f5 = 3rr--2?r+~r~ all (6~)~ < 415 .

m-4

(13

(174

From (17~)

B(r- + u, (67r)-) 5 5B(r- + ~,3a-2~+~~)

(18) 5 5B(r- * 5 charged-prongs) ,

and from (17a) and (17c),

B(r + ur 7r-57r”) 5 (9/7)B(r- + u, 3?r-2~+~‘)

(19) I (9/7pq- + 5 charged-prongs) .

11

Alternately, since six pions are produced through the hadronic vector current

we can use e+e- -+ 67r data to directly calculate r- + ur (6~)~. The e+e-

datalg are not very accurate, but they indicate a cross section for 67r production

of a few nanobams for center-of-mass energies below m,.. If we take 1Onb as a

reasonable upper limit for a(e+e- + 67r) from 1.4 GeV to mr, then I’(r- +

u~(67r)-)/r(7- -- + ur e uc) < 0.024. This is negligible from the point of view of

having an impact on the considerations in the next section.

(K) r + u, (Kx)-

The decay r- + ur K°K- occurs through the weak vector current and hence the . c-

rate for this process can be related to the cross section for e+e- + KK occurring

through the action of the isovector part of the electromagnetic current. Unfor-

tunately the process e+e- --) ICr also occurs through the action of the isoscalar

part of the electromagnetic current: in fact for Q M 1 GeV it is dominated by the

presence of the 4. Sorting out the two contributions requires at least data on both

e+e- --) K+K- and e+e- --) Ki$, but the data on the latter process are sparse.

If we nevertheless blindly proceed and assume that above 1.2 GeV the isoscalar

and isovector contributions are equal (adding in e+e- -+ K+K- and cancelling

in e+e- + I$Ko,), then integration over the measured a(e+e- + K+K-) as in

Eq. (6) yields a branching ratio for r- + u, K’K- of - 0.5%.

We note that due to the decay I$ --+ 7r+r-, one third of these involve three

charged-prongs. The upper limit 2o of 0.6% on B(r- + u, K-rr+rrr-) then puts

an experimental limit of 1.8% on B(r- + u, K’K-).

This mode must be present inasmuch as the p’, which is an important part of

12

the four pion state in r- -+ ur (47r)- also decays into K*K and K *K and thus

feeds T- + u, (K*K)- and r- -+ ur (K*K)- at an expected branching ratio

of g 1%. Indeed the observation 21-23 of r- ---) ur K+K-I~- is consistent with

being of this origin with a branching ratio - 0.2%.

The constraints due to isotopic spin conservation (which hold whatever is the

dynamics) limit the KICK charge states to obeyl’

0 I fKOprO = KOK-IrO

< 112 , all (Kx?r) -

PK%r- 0 I fKOROr- = all (KK r) - L 314 ,

0 2 jK+K-r- = K+K-r-

- all (KK T)-

5 314 . (204

However one charged-prong decays arise both from K°K-x0 (two-thirds of the

time) and from K°Kolr- (four-ninths of the time), and a calculation of the max-

imum (or minimum) fraction of r ---) Kx?r decays which result in one charged-

prong demands that we look at their joint distribution.

This is shown in Fig. 4, where the shaded interior of the ellipse is the allowed

region. The fraction of one charged-prong decays is given by

fl = ; fKOXOr- + ; fK”K-r” ,

and would appear as a diagonal line with slope -3/2 in Fig. 4. The quantity fr

4 13 ..Y

is maximal when this line is just tangent to the ellipse, which occurs when

jl = (1+ &)/(3@ = 0.526 ,

f3 = (5 - 6)/g ,

and

f5 = (1 + 1h)/(246) .

(M) T- + ur (Km)-

This is the Cabibbo-suppressed analogue of r- --) u, (37r)

due to isospin conservation are:

.-- l/3 < ~K-T+~-- =

K-lr+7F < 213 , all (Km)- -

0 5 jK-rOrO = K-&P

< 113 , all (Km)- -

0 I fxoror- = K07r0?f-

< 213 . all (Km)- -

(21)

The constraints l7

(224

w4

(22c)

The upper bound on r + u, K-lr+r- noted above20’23 and Eq. (22a) imply

B(r + u, Km) < 1.8%.

Both the channels K-r”no (always) and K”norr- (two-thirds of the time)

generate one charged-prong r- + u, (Kmr)- decays. Their joint distribution is

very simply the linear relation

3 jK-+‘+’ + ; fKoror- = 1 , (23)

while the fraction of one charged-prong decays is

2 ..w fl = fK-+‘sO + 3 fKoToT- . (24

14 4 ..Y

The maximum of jr occurs when j~o,o,- is a maximum (F 2/3), at which point

fl = 419 and j3 = 519. (25)

3. Summary and Comparison with Experiment

The various r decay modes we have considered are summarized in Table I.

For the seven modes above the dashed line we have calculated their branching

ratio in terms of the branching ratio for r + u, e Do, which we have assumed

to be 17.9%. In contrast, for the six modes listed below the dashed line we _ z--

have chosen either to give upper limits on their branching ratios or to list the

three charged-prong branching ratio as an unknown quantity (5, y, z, or w) and

to insert the corresponding upper bound that ensures for the one charged-prong

branching ratio.

The reason for normalizing the rates above the dashed line to that for r ---)

ur ep’, is that they are all calculable from data obtained outside of r decay. These

data are mostly more accurately known experimentally than are the correspond-

ing r branching ratios. In particular r --) u7 k VP, r + u,z and r --+ u, K are

calculable in terms of r + u, e V, to very high accuracy and these four modes

together account for almost half of all r decays. For one charged-prong decays

only r + u, KTR, r + ur KT and r -+ u, 47r have predicted branching ratios in

terms of r -+ u, eu, for which the input data do not have tiny errors. In the case

of r + ur KT and r + ur 47r the one charged-prong portions of their branch-

ing ratios are of order l%, and even a f20% error in the prediction has little

effect on the overall one charged-prong branching fraction of the 7. Only for

15

r + ur zz is the branching ratio big and the error on the input, a(e+e- + zz),

not tiny. Here a HO% error on the input cross section would mean a f2% error

in the prediction for B(r + u, zz) and thus in the one charged-prong branching

fraction. Furthermore, while the decay rates themselves depend strongly on m,,

their ratios to I’(7 + ur e v,) depend very weakly on mT.

It should be immediately pointed out, however, that within errors all the pre-

dicted branching ratios above the dashed line are in agreement with experiment.6

For example B(r -+ u, rr) = 10.9% in Table I is to be compared to 10.3 f 1.2%

of the Particle data group’ and B(r -+ ur rrrz) = 22.0% is to be compared to6

22.1 f 2.4% or to the new MkII number reported in Ref. 3 of 22.0 f 0.8 f 1.9%. . k--

Now comes the problem. Accepting the input hypotheses to Table I, the

sum of the one charged-prong branching ratios for the decay modes above the

dashed line is 71.0%, while the corresponding three charged-prong number is

5.2%. On the other hand, the world average value3 of the total one charged-

prong branching fraction of the r is 13.7 f 0.5%, and correspondingly” for the

three charged-prongs it is 86.3f0.5%. Therefore 15.3% of the one charged-prong

decays and 8.5% of the three charged-prong decays must come from modes below

the dashed line in Table I (or other modes yet). However, of the modes below

the dashed line, only r + ur 37r is sizeable and its contribution to three charged:

prongs (denoted by x in Table I) is always larger (by isospin) than its contribution

to one charged-prong.

Thus if r -+ u, 37r accounted for the remaining 8.5% of three charged-prong

decays, one would still have at least 15.3 - 8.5 = 6.8% of r decays which go

to one charged-prong to account for. The remaining r decay modes below r +

u, 37r in Table I all are small, have small contributions to the one charged-prong

16

branching fractions, and even if they weren’t small, all have at most comparable

contributions to one charged-prong and three charged-prong decays.

In fact, the average of recent measurements3 of B(r- --) u, rr-?r-rr+) from

DELCO and MAC is 6.4 f 0.7% so that the three charged-prong decays of the

r are almost accounted for within errors. 24 As this decay is known to be over-

whelmingly r 3 ur~p, B(T- + u,~~~~c/r~) = B(T- + u,T-K~~T+). Even

allowing the sum of the modes listed below r + u, 37r to contribute a total of

2% to one charged-prong r decays, we have - 6% of 7 decays going into one

charged-prong for which we do not account.

This situation has been examined previously25-27 with some indication of a a- . -

problem. 2’ Previous summations 25926 of exclusive r modes purely from experi-

mental data for each mode involve a considerably larger statistical error since they

generally do not take into account the correlation in branching ratios imposed

by data from outside r decay, as well as some individual modes involving multi-

neutrals have large errors. The discrepancy in the one charged-prong decays is

then much less statistically significant when things are done in this way. Also,

without the bounds on r + u, 57r and r --) ur 67r we derived, these modes could

have made up any discrepancy. In addition, the error bars on the measurement

of the inclusive one and three charged-prong branching fractions have recently

shrunk considerably, 3 making the problem more acute. A possible discrepancy

of - 10% in one charged-prong decays was pointed out in Ref. 17. However, the

recent data do not indicate (see Table I) a significant difference between the con-

tributions from the vector current (- 28% known) and the axial-vector current

(- 24% known) which was used in Ref. 27 to indicate that the affect originated

in the axial-vector current.

17 - . ..y

What are the possible explanations ? First, the branching ratio for r +

u, ec’, could be larger than the 17.9% used in Table I. For example, Table II

shows what happens when B(r + u, eve) = 19.0%. The sum of one charged-

prong branching fractions above the dashed line goes up to 75.4%. Including

B(r- + u,~~?r~~~) at the 6.4% level and taking 2% for the sum of the one

charged-prong contributions of the modes listed below r + ur 37r removes any

statistically significant discrepancy. It should be noted however that many of the

branching ratios above the dashed line in Table II are at the upper limits of the

experimental error bars.

Second, note in particular the large mode r + u, XT, for which the prediction

. ze relative to r + ur ev’, has the possibility of error due to errors in a(e+e- + XX).

-However, if in Table I the discrepancy is to be “solved” by increasing this mode

alone (raising B(r + u,rr) by - 6%), then the input a(e+e- + rr+?r-) must

have been too low by - 30% and the “true” B(r --$ u, XT) would be three or

more standard deviations above the present measurements.3

Third, the r could have conventional decay modes which we have not con-

sidered so far, e.g., r- + ur VK-~F’, or the mode r + u, qqr considered in Ref.

27. Such decays would mostly appear as one charged-prong decays and although

the former process is related in strength to e+e- + q?r+lr-, it seems this might

have been missed. There is furthermore no reason to assume that such r decays

would have comparatively large branching fractions, aside from fixing up the

discrepancy in the one charged-prong branching fraction.

Fourth, the r could have decays which are unconventional. Decays such as

r- + u, S- , where S- is “elementary” (i.e. pointlike) and either stable or

unstable, are ruled out by the lack of evidence for e+e- ---) S+S- and an increase

18

in R above that which is expected from the known quarks at high energies. If

the S- were virtual however, and coupled mostly to particles which manifest

themselves as one charged-prong at low masses, it might provide an explanation.

The experimental path to settle the question of a possible discrepancy is

fairly clear. We need a better determinations of B(r + u, eve) and/or B(r +

u, pup) in the clean PETRA/PEP environment. If the discrepancy persists, one

should then check whether the “extra” decays are in 7 + one charged-prong with

photons or without photons, with one 1~’ or with more than one K’, etc. With

thousands of clear e+e- + r+r- events produced, a decay mode with a branching

ratio of order 5% should be fairly easily detected. Experiments in the relatively

. c near future should tell us whether the discrepancy in one ,charged-prong decays

- of the r is a statistical accident or will lead us to interesting new decays of the r.

ACKNOWLEDGEMENTS

We thank J. Dorfan, G. Feldman, R. Madasas, M. Peshkin, A. Read, J.

Rosner, W. Ruchstuhl, and J. Smith for discussions.

19 . ..Y

REFERENCES

1. M. L. Perl, Ann. Rev. Nucl. Part. Sci. 30, 299 (1980).

2. J. Jaros, talk at the Topical Conference of the 1984 SLAC Summer Insti-

tute on Particle Physics, July 23-August 3, 1984 (unpublished) reviews the

measurements of the r lifetime.

3. W. Ruckstuhl, talk at the Topical Conference of the 1984 SLAC Summer

Institute on Particle Physics, July 2bAugust 3, 1984 (unpublished) reviews

the data on r decays.

4. Y. S. Tsai, Phys. Rev. D4, 2821 (1971); H. B. Thacker and J. J. Sakurai,

Phys. Lett. m, 103 (1971).

5. K. Gaemers and R. Raitio, Phys. Rev. U, 1262 (1976); T. Hagiwara et

ul., Ann. Phys. (N.Y.) 106, 134 (1977); F. J. Gilman and D. H. Miller,

Phys. Rev. m, 1846 (1978); T. N. Pham et al., Phys. Lett. m, 623

(1978); N. Kawamoto and A. Sanda, Phys. Lett. a, 446 (1978).

6. Particle Data Group, Rev. Mod. Phys. 56, No. 2, Part 11 (1984).

7. F. J. Gilman and D. H. Miller, Ref. 5 and unpublished calculations with

the present value of m,.

8. T. Das, V. S. Mathur, and S. Okubo, Phys. Rev. Lett. l8, 761 (1967).

9. The numerical integration results in Eqs. (12a) and (12~) show that over

half the contribution comes from 47r masses below 1.4 GeV. We thank Jim

Smith for discussions on this point.

10. V. Sidorov, Proceedings of the 1979 International Symposium on Lepton

and Photon Interactions at High Energies, August 23-29, 1979, T.B.W.

Kirk and H.D.I. Abarbanel, eds. (Fermilab, Batavia, 1979), p. 490.

20

11. J. E. Augustin et crl., Orsay preprint LAL/83-21, 1983 (unpublished).

12. C. Bacci et al., Nucl. Phys. B184, 31 (1981).

13. G. Cosme et al., Nucl. Phys. B152, 215 (1979).

14. Recent measurements from the MkII and DELCO collaborations show the

37r mass distribution to be dominated by a broad Al(JP = l+) peak (with

mass - 1100 MeV) . See Ref. 3 and the previous measurements in Ref. 6.

15. Y. S. Tsai, Ref. 4; T. N. Pham et al., Ref. 5; N. Kawamoto and A. Sanda,

Ref. 5.

16. T. N. Pham et al., Ref. 5.

17. M. Peshkin and J. L. Rosner, Nucl. Phys. B122, 144 (1977). We thank M.

Peshkin and J. L. Rosner for the use of the their computer program to find

isospin restrictions on charge distributions and several discussions.

18. The MAC collaboration reports a 95% CL limit: B(r + 5 charged-prongs)

< 0.16%. See Ref. 3.

19. B. Delcourt et al., Orsay preprint LAL 81/28, 1981 (unpublished); C. Bacci

et al., Ref. 12.

20. H. Aihara et al., LBL preprint LBL-18014, 1984 (unpublished). We thank

R. Madaras for a discussion of the applicability of the TPC result to r- +

u, K-K;.

21. DELCO collaboration, see Ref. 3 and also the event reported in Ref. 20.

22. Both the vector and axial-vector currents can contribute to this mode.

23. DELCO collaboration reports B(r- + u7 K+K-T) = 0.22fi::,7 % and

B(r- + u, K-T+T-) = 0.22::::: %. See Ref. 3.

21

24. Combining the possible error in the calculation of B(r- + u, ?r-xr-xr+xo)

with the measurement error in B(r- --) ur ~-T-K+) already allows consis-

tency within errors with the branching fraction for three charged-prongs,

together with small contributions from r + u, 57r, r -+ u, Kmr, etc.

25. C. A. Blocker et al, Phys. Rev. Letters 49, 1369 (1982).

26. H. J. Behrend et al, DESY preprint DESY 84-008, 1984 (unpublished).

27. T. N. Truong, SLAC preprint SLAC-PUB-3341, 1984 (unpublished).

FIGURE CAPTIONS

. a- 1. Data for a(e+e- --) 27rr+27r-) from Novosibirsk lo (*), Orsay l1 (A) and

Frascati12 ( l ) as a function of center-of-mass energy, Q.

2. Data for a(e+e- + R+~T-~~?T’) from Novosibirsk lo (*) , Frascati l2 ( l ) , and

Orsay l3 (A) as a function of center-of-mass energy,Q.

3. Region (shaded) allowed by the constraint of isospin conservation in r- -+

u, (57r)- for the fraction j ,r-I-r-I+r+ versus the fraction j~-T~~~~~l~.

4. Region (shaded) allowed by the constraints of isospin conservation in r- +

u, (KKlr) for the fraction jKopr- versus the fraction ~KOK-~O.

22

Table I

T decay branching ratios assuming B(T + vT ep,) = 17.9%

Decay Mode Branching Ratio (%)

1 Charged-Prong 3 Charged-Prongs

Source

r- + u7e-tie

r- + WqL

r- + u77r-

-7”- --+ u,K-

r- -+ uT(7r7r)-

r- -+ vz(Kr)-

r- + vT(47r)-

17.9 -

17.4 -

10.9 -

0.7 -

22.0 -

1.1 0.3

1.0 4.9

r- + v7(37r)-

r- 4 vT(57r)-

r- + +(67r)-

r- --) vT(KK)- -

r- --) v,(KKr)-

r- -+ z+(Kmr)-

5% X

< 0.12 Y

< 0.21 < 0.64

< 1.2 < 0.6

< 1.29 y Y

<4/5 w W

Input

Eq. (3)

Eq. (4)

Eq. (5)

Eq. (7)

Eq. (9)

Eqs. (13)

Eqs. (14)

Eq. (16) and Ref. 18

Eqs. (17),( 19) and Ref; 18

Ref. 20

Eq. (21)

Eq. (25)

23

Table II

r decay branching ratios assuming B(r ---) v, en,) = 19.0%

Decay Mode Branching Ratio (%)

1 Charged-Prong 3 Charged-Prongs

Source

r- + -- u,e ue 19.0 -

r- + wq4 18.4 -

r- --+ urn- 11.6 -

-r-j u7K- 0.8 - 3’

r- - uT(7r7r)- 23.4 -

r- ---) uT(Kr)- 1.2 0.3

r- + u7(47r)- 1.0 5.2

-------- -------- - ---- --

r- ---, uT(37r)-

r- --) u7(57r)-

r- + u7(67r)-

r- --) u7(KK)-

r- + u,(KKr)-

r- + u,(Kmr)-

IX X

< 0.12 Y

< 0.21 < 0.64

< 1.2 < 0.6

< 1.29 z z

< 0.8 w W

Input

Eq. (3)

Eq. (4)

Eq. (5)

Eq- (7)

Eq. (9)

Eqs. (13)

Eqs. (14)

Eq. (16) and Ref. 18

Eqs. (17),( 19) and Ref. 18

Ref. 20

Eq. (21)

Eq. (25)

24

50

40

b 20

IO

-0 I .o 1.2 1.4

Q (GeV) 1.6 1.8

4813Al

Fig. 1

60

50

40 z

2 30 b

. +- 20

IO

I I I

-

0 1.0 1.2 1.4 1.6 1.8

5-04 Q (GeV) 41313A2

Fig. 2

0.7

0.6

0.5

;k 0.4

lb P

‘k k 0.3

0.2

0.1

0 0 0.1

5-84

0.2 0.3 f 7r-7T07r07roTTo

Fig. 3

0.4 4813A4

‘k l 06

i.!x 0 . a- -x

+- 04 .

5-84

Fig. 4

4813A3